TrojanPoem
  • TrojanPoem
Prove that : A, B, C > 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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TrojanPoem
  • TrojanPoem
|dw:1434890770639:dw|
TrojanPoem
  • TrojanPoem
The value of the det is (A + B + C)^3
dan815
  • dan815
expand it

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TrojanPoem
  • TrojanPoem
I found it's value with the tri method.
TrojanPoem
  • TrojanPoem
(A+B+C)^3
dan815
  • dan815
|dw:1434891229492:dw|
TrojanPoem
  • TrojanPoem
We have to prove that , The given is A , B, C > 0 so we can say their sum is also > 0 (A+B+C)^3 > 0
TrojanPoem
  • TrojanPoem
But expanding this A + B +c will take up to decade .
dan815
  • dan815
here is a method to show this is true
TrojanPoem
  • TrojanPoem
What's the method ?
dan815
  • dan815
lets say ABC are all approaching the same number,
dan815
  • dan815
|dw:1434891532175:dw|
dan815
  • dan815
now u were to begin varying B and C,
dan815
  • dan815
we can rewrite B and C as A-k
dan815
  • dan815
and lets Say we always make sure that A is always the biggest number or equal
TrojanPoem
  • TrojanPoem
So we will make assumption that A > b,c and b, c are approaching A
TrojanPoem
  • TrojanPoem
I have problem with electricity , I will re-log soon , sorry.
dan815
  • dan815
you can begin cancelling terms now
dan815
  • dan815
oh apparently there is a neat solution to this
dan815
  • dan815
|dw:1434892463880:dw|
dan815
  • dan815
for positive numbers
dan815
  • dan815
heres a proof for the binomial case, maybe u can spend some time to prove it for the trinomial
dan815
  • dan815
|dw:1434892832161:dw|
TrojanPoem
  • TrojanPoem
This is the arthmetic , geometric sequence inequality right ?
TrojanPoem
  • TrojanPoem
The Arithmetic mean is always greater than the geometric mean
TrojanPoem
  • TrojanPoem
But can you write the proof of this inequality ?
dan815
  • dan815
id have to work it out too,
TrojanPoem
  • TrojanPoem
Are you good with maxima and minima applications and complex number ?
dan815
  • dan815
sure : )
TrojanPoem
  • TrojanPoem
I will open a new question

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